A random sample of 100 adult men in Toronto was randomly selected.The sample correlation between their heights and weights was found to be 0.62.Ten subsequent bootstrap samples based on this initial sample produced the following correlation coefficients: 0.58,0.52,0.67,0.62,0.63,0.54,0.71,0.66,0.58,0.70.Based on these ten resamples,find the bootstrap of the standard error of the sample correlation.
A)0.0206
B)0.2222
C)0.6210
D)0.0043
E)0.0652

Question

Quizplus · Accepted Answer

The standard error of the sample correlation can be estimated using the standard deviation of the bootstrap samples. First, calculate the mean of the bootstrap samples: (0.58 + 0.52 + 0.67 + 0.62 + 0.63 + 0.54 + 0.71 + 0.66 + 0.58 + 0.70) / 10 = 0.621. Then, calculate the variance: [(0.58-0.621)^2 + (0.52-0.621)^2 + (0.67-0.621)^2 + (0.62-0.621)^2 + (0.63-0.621)^2 + (0.54-0.621)^2 + (0.71-0.621)^2 + (0.66-0.621)^2 + (0.58-0.621)^2 + (0.70-0.621)^2] / 9 = 0.00424889 (using Bessel's correction with n-1 in the denominator for an unbiased estimate). The square root of the variance gives the standard deviation, which is the standard error of the sample correlation: sqrt(0.00424889) ≈ 0.0652.

A Random Sample of 100 Adult Men in Toronto Was